High energy density vibration energy harvesting device with high-mu material

ABSTRACT

The present disclosure describes a vibration energy harvester with increased output power density. The vibration energy harvester has two magnetic solenoids, each with cores that include multiple layers of high permeability materials. The two magnetic solenoids are fixed at two sides of a movably supported hard magnetic core, such as a magnet pair with anti-parallel magnetization, which produces a spatially inhomogeneous bias magnetic field for switching the flux inside the solenoids during vibration of the magnetic core. An output voltage of 2.52 V and a power density 20.84 mW/cm3 at 42 Hz, with a half peak working bandwidth of 6 Hz.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a continuation of and claims the benefit of andpriority under 35 U.S.C. §119(e) to U.S. patent application Ser. No.13/554,263, filed on Jul. 20, 2012, and entitled“High Energy DensityVibration Energy Harvesting Device with High-mu Material,” and to U.S.Provisional Application No. 61/510,781, filed on Jul. 22, 2011, andentitled “High Energy Density Vibration Energy Harvesting Device withHigh-mu Material,” the disclosures of which are hereby incorporatedherein by reference in their entirety.

FIELD OF THE INVENTION

The present disclosure relates generally to high energy densityvibration energy harvesting devices with high-mu materials.

BACKGROUND

Vibration energy harvesting technologies are developing rapidly, showinggreat potential in many different applications. For example, miniaturevibration energy harvesters are often used for applications such asautonomous sensors and system on chip applications. Most applicationsuse one of four major vibration energy harvesting mechanisms, includingelectromagnetic, electrostatic, magnetoelastic, and piezoelectricmechanisms. However, such vibration energy harvesters achieve differentoutput powers and energy densities. For example, piezoelectric-basedvibration energy harvesters often demonstrate a much higher energydensity than other counterpart mechanisms, reaching ˜6mW/cm³.Specifically, some piezoelectric bare beam based vibration energyharvesters can generate a power of 6.63 mW/cm³. Because of this,piezoelectric-based vibration energy harvesters are often more widelyused than other forms of vibration energy harvesters. However, they cansuffer from narrow bandwidth (or a limited operating frequency range of2-5% of the center operating frequency), degraded polarization afterprolonged use, and/or the negative side-effects caused by a brittlecantilever.

SUMMARY

In one aspect, an energy harvesting device, includes a first and secondsolenoid, each solenoid including (a) a wire coil wrapped around (b) ahigh permeability core with two or more layers, and the first and secondsolenoid being disposed along a first path, and a magnetic core:disposed between the first and second solenoid such that the firstsolenoid is mounted on a first side of the magnetic core, and the secondsolenoid is mounted on a second side of the magnetic core, and mountedon a support such that the magnetic core can vibrate along a second paththat intersects the first path, vibration of the magnetic core inducinga flux change in the first and second solenoids.

In one aspect, in an energy harvesting device, including (1) a first andsecond solenoid, each solenoid including (a) a wire coil wrapped around(b) a high permeability core with two or more layers, and the first andsecond solenoid being disposed along a first path, and (2) a magneticcore disposed between the first and second solenoid such that the firstsolenoid is mounted on a first side of the first magnet, and the secondsolenoid is mounted on a second side of the first magnet, the magneticcore being mounted on a support such that the magnetic core can vibratealong a second path that is orthogonal to the first path, a methodincludes vibrating the magnetic core along the second path to induce aflux change in the first and second solenoids.

In one or more embodiments, the magnetic core includes a first magnet.

In one or more embodiments, the magnetic core includes a second magnetdisposed above the first magnet such that the first magnet and secondmagnet have anti-parallel moments.

In one or more embodiments, the support includes a spring.

In one or more embodiments, the spring includes a circularcross-section.

In one or more embodiments, the spring has a resonance frequency of 42Hz.

In one or more embodiments, vibration of the magnetic core achieves apower output density of 20.84 mW/cm³.

In one or more embodiments, each high permeability core is a 28-layercore, each layer including dimensions 2 cm×2 cm×0.002 inch.

In one or more embodiments, the magnetic core includes a second magnet,and the first and second magnets are SmCo magnets with dimensions 2.2cm×1.3 cm×0.2 cm.

In one or more embodiments, a total volume of the energy harvestingdevice is 6.44 cm×3.25 cm×1.4 cm=29.3 cm³.

In one or more embodiments, the first solenoid, the second solenoid, andthe support are mounted to a base such that the first path issubstantially parallel to the base, and the second path is substantiallyperpendicular to the base.

In one or more embodiments, the first and second solenoids include asame size.

In one or more embodiments, the first and second solenoids include asame shape.

In one or more embodiments, the first and second solenoids are joined inseries to double a voltage of the energy harvesting device.

In one or more embodiments, the magnetic core is vibrated at 42 Hz, andan output power of 610.62 mW is generated.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and advantages of the present invention willbe apparent upon consideration of the following detailed description,taken in conjunction with the accompanying drawings, in which likereference characters refer to like parts throughout, and in which:

FIG. 1 is a table that lists different comparison metrics for variousvibrating energy harvesting mechanisms in accordance with certainembodiments;

FIG. 2A is a schematic of an energy harvesting device in accordance withcertain embodiments;

FIG. 2B is a schematic of the energy harvesting device of FIG. 2A withits magnetic core in an upper position in accordance with certainembodiments;

FIG. 3A is a top-view image of an energy harvesting device in accordancewith certain embodiments;

FIG. 3B is a side-view image of the energy harvesting device of FIG. 3Ain accordance with certain embodiments;

FIG. 4 is a graph of open circuit voltage (V) of the energy harvestingdevice of FIGS. 3A-3B over time (s) using three different springs inaccordance with certain embodiments;

FIG. 5 is a graph of the output power (mW) of the energy harvestingdevice achieved using the three springs graphed in FIG. 4 in accordancewith certain embodiments; and

FIG. 6 is a graph of the power density (mW/cm³) of the energy harvestingdevice based on the frequency (Hz) of the support in accordance withcertain embodiments.

DETAILED DESCRIPTION OF THE INVENTION

The present disclosure provides for magnetic-based vibration energyharvesters that achieve a high energy density by using high permeabilitymagnetic materials. While a piezoelectric bare beam based vibrationenergy harvester can generate a power energy density of 6.63 mW/cm³,theoretically the magnetostatic energy density (½μH²) in highpermeability magnetic materials is 10⁵-10⁶ times that of theelectrostatic energy density (½εE²) in piezoelectrics. Suchmagnetic-based vibration energy harvesters can achieve, for example, aenergy density greater than 20 mW/cm³ (e.g., with an acceleration of 5g), which is over 3 times the energy density of known vibration energyharvesters.

Before describing in detail the particular components of magnetic-basedvibration energy harvesters, in some embodiments the vibration energyharvesters include two fixed solenoids. Each solenoid has a multi-layerhigh permeability solenoid core. A vibrating magnetic core is disposedbetween the two fixed solenoids. The multilayer high permeabilitysolenoid cores lead to significantly increased flux change in thesolenoid within one period of vibration of the magnetic core than othersuch devices, without increasing the total volume of the device. Inaddition, the two solenoids at both sides of the vibrating magnet(s)make full use of the spatially inhomogeneous bias magnetic fields atboth sides of the magnets, leading to doubled power output, and adramatically enhanced power density than previous energy harvesters.

FIG. 1 is a table 100 that shows metrics of comparison among variousvibrating energy harvesting mechanisms. The mechanisms/products includeelectrostatic, magnetoelectric, piezoelectric, magnetoelectric sensorbased, magnetostrictive, perpetuum, KCF (from KCF Technologies of StateCollege, Pa.), and high permeability (High-μ (1^(st) gen), and High-μ(2^(nd) gen)) material-based energy harvesting devices. The metrics ofcomparison include the central frequency f_(center), measured in Hz;acceleration “a,” measured in g (9.8 m/s²); P_(max), the maximum outputpower of the device, measured in mW; and power density, measured inmW/cm³. As shown in table 100, the 2^(nd) generation high-μ vibrationenergy harvester (e.g., which includes two fixed solenoids withmulti-layer high permeability cores, and a vibrating magnetic core, asdescribed herein) has the largest output power density of 20.84 for anf_(center) of 42 Hz. Such a power density is over three times largerthan the widely used piezoelectric device. Further, the performance ofthe High-μ (2^(nd) gen) device is greater than that of the High-μ(1^(st) gen) device (e.g., upwards of 10× the flux change of the High-μ(1^(st) gen) device). The High-μ (2^(nd) gen) device uses two stationarysolenoids with thicker multi-layer high-μ magnetic core materials (e.g.,20 layers of material), which allows a greater flux change to be inducedin one vibration of the magnetic core. In contrast, the High-μ (1^(st)gen) device has a single vibrating solenoid, and therefore the solenoidcore can not be thick, resulting in less flux change.

FIG. 2A is a schematic of an energy harvesting device 200 in accordancewith certain embodiments. The energy harvesting device 200 includes afirst solenoid 202A and a second solenoid 202B (indicated by respectivedotted rectangles for ease of reference, and collectively referred toherein as solenoids 202). Each solenoid 202 can include a wire coil(204A, 204B) wrapped around a multi-layer high permeability (high-μ)core (206A, 206B). The energy harvesting device 200 includes a magneticcore 208, which is disposed between solenoid 202A and solenoid 202B.Solenoid 202A is mounted to the base 220 on the left side of themagnetic core 208 via mount 210A, and solenoid 202B is mounted to thebase 220 on the right side of the magnetic core 208 via mount 210B. Themagnetic core 208 is mounted to the base 220 via support 212 such thatthe magnetic core 208 can vibrate between the solenoids 202. While twosolenoids 202 are shown in device 200, any number of solenoids can beused for a particular energy harvesting device (e.g., 1, 3, etc.).Further, the configuration shown in FIG. 2A is intended to be exemplaryonly, and is not intended to be limiting. One of skill can appreciatethat other variations of energy harvesting devices can be engineeredaccording to the principles described herein without departing from thespirit of the description.

In some embodiments, the solenoids 202 are manufactured to have the samesize (e.g., the same three dimensional size) and/or shape (e.g., thesame number of layers in the cores 206A, 206B, and the same number ofcoil layers for each coil 204A, 204B, the same number of rotationsaround the core per coil layer, and/or the like). In some embodiments,the multi-layer high permeability cores (206A, 206B) are formed ofmultiple layers of a non-oriented 80% nickel-iron-molybdenum alloy,which offers extremely high permeability. The material can be fabricatedusing hydrogen annealing to maximize permeability. In some embodiments,the high permeability materials are foils provided by The MuShield®Company of Londonderry, N.H. (e.g., foil with thicknesses of 0.002″,0.004″, 0.006″, and/or 0.010″). Any high permeability magnetic materialscan be used as the magnetic core for the energy harvester to achievesimilar harvester performance. (e.g., ferrite or other inductor corematerials).

The magnetic core 208 includes magnets 214 and 216. Magnet 214 isdisposed above the magnet 216 such that the magnets have anti-parallelmoments (e.g., the North (N) pole of magnet 214 is disposed above theSouth (S) pole of magnet 216, and the South (S) pole of magnet 214 isdisposed above the North (N) pole of magnet 216). The magnets 214, 216are joined by joining portion 218 (e.g., which can be made from amagnetic or a non-magnetic material). In some embodiments, the support212 is a spring (e.g., with a circular cross-section, a squarecross-section, and/or the like). While the magnetic core 208 is shownwith two magnets 214 and 216, the magnetic core can include any numberof magnets. For example, in some embodiments, the magnetic core 208includes one magnet, or three or more magnets. Further, the magnets canbe arranged in other ways than with anti-parallel moments. For example,the magnets can be oriented such that the same moments are aligned(e.g., N above N, and S above S). As another example, the magnets can bepartially crossed, such that they do not completely overlap witheachother (e.g., to form an “X” shape).

Vibration of magnetic core 208 creates a voltage V across the solenoids202. As the pair of magnets 214, 216 vibrate up and down, the magneticfield lines inside each solenoid 202 change direction periodically,inducing a large magnetic flux change (M) in both solenoids 202. Themagnetostatic coupling between the solenoids 202 and the time varyinginhomogeneous bias magnetic field results in a nonlinear oscillation anda complete magnetic flux reversal in the solenoids 202. The presence ofthe multi-layer highly permeable cores dramatically increase themagnitude of magnetic flux inside the coils of the solenoids 202. Theinduced voltage can be doubled to form voltage V by connecting the twosolenoids in series.

FIG. 2B is a schematic of the energy harvesting device 200 of FIG. 2Awith the magnetic core 208 in an upper position. As shown in FIGS.2A-2B, the solenoids 202 are disposed along first path 250. In someembodiments, the first path 250 is substantially horizontal to thesurface plane of the base 220. Magnetic core 208 can vibrate along asecond path 252 that intersects (e.g., is orthogonal to) the first path250. In some embodiments, the second path 252 is substantiallyperpendicular to the surface plane of base 220. As shown by arrows 254A,254B, vibration of the magnetic core along path 252 induces a fluxchange in the solenoids 202 (e.g., arrows 254A, 254B point to the rightin FIG. 2B, compared to the arrows in FIG. 2A which point left, due tothe movement of the magnetic core 208 to an upward position along thepath 252. The mass of the hard magnetic core 208, the stiffness of thesupporting spring, and/or the magnetostatic coupling between thesolenoids 202 and/or hard magnetic core 208 can determine the resonancevibration frequency and the output voltage of the energy harvester.

While paths 250, 252 are shown as straight paths in FIG. 2B, in someembodiments the paths are nonlinear paths. For example, an equivalentstand-alone spring-mass system becomes a nonlinear oscillation systemonce introduced into the energy harvesting device 200 due to themagnetostatic coupling between the solenoids 202 and the hard magneticcore 208. This nonlinear effect can be explained, for example, from apotential energy point of view. The elastic potential energy of astand-alone spring-mass system is a well-know linear relationship, withonly one minimum value, which happens when the mass passes theequilibrium position in the middle. In contrast, the magnetostaticpotential energy has two identical minimum values due to the couplingbetween the magnet(s) and solenoids, which appear when the magnet(s)move a short distance up or down from the equilibrium position in themiddle. As a result, the superposition of two different types ofpotential energy make a nonlinear relationship, leading to a wideroscillation frequency range.

In some embodiments, the total induced voltage of the energy harvestingdevice equals the integral over the whole solenoid, because the magneticfield magnitude varies along the axis. The open circuit voltage, V, canbe expressed by Equation (1):

$\begin{matrix}\begin{matrix}{V = {2\frac{{\phi (t)}}{t}}} \\{= {2\frac{{\int{\left\{ {{H\left\lbrack {x,{y(t)}} \right\rbrack} + {4\pi \; {M\left\lbrack {x,{y\left( {x,t} \right)}} \right\rbrack}}} \right\} \cdot A \cdot {N}}}}{t}}} \\{{= {2\frac{{\int{4\pi \; {{M\left\lbrack {x,{y\left( {x,t} \right)}} \right\rbrack} \cdot A \cdot {N}}}}}{t}}},}\end{matrix} & (1)\end{matrix}$

where:dφ(t)=the magnetic flux change over time;dt=time;H[x,y(t)]=the magnetic field H at time t, at the spatial positiondefined by the point (x (along the length of the solenoid), y (along thedirection the vibrating magnetic core travels));M[x,y(x,t)]=magnetization M as a function of time t at coordinates x,y(x,t);A=the total cross section area of the multilayer cores of the solenoids;anddN=the number of loops in the infinitesimal length unit of the solenoid,which can be calculated according to Equation (2):

dN=N _(L) ·dx/d _(w).   (2)

where:N_(L)=the number of loop layers of the coil;dx=the position x along the length of the solenoid; andd_(w)=the copper wire diameter.

Hence, the maximum output power P_(max), which happens when the loadimpedance equals the conjugate of the output impedance of the solenoidcoil R_(coil), is defined by Equation (3):

$\begin{matrix}\begin{matrix}{P_{\max} = \frac{\left( \frac{V}{2} \right)^{2}}{R_{coil}}} \\{{= {\frac{16S}{R_{coil}}\left( {A^{\prime}\pi \frac{N_{L}}{d_{w}}} \right)^{2}\left( {\int_{0}^{L}{\left\{ \ \frac{{M\left\lbrack {x,{y\left( {x,t} \right)}} \right\rbrack}}{t} \right\} {x}}} \right)^{2}}},}\end{matrix} & (3)\end{matrix}$

where:R_(coil)=the resistance of the solenoid;S=the number of layers in each core;A′=the cross section area of one layer of the core;L=the length of the solenoid; andd_(w)=the diameter d of the wire w.

Equation (3) shows that the output power P_(max) increases as thevibration frequency increases (e.g., if all other parameters are keptconstant). In some examples, when using the same source power, theamplitude decreases if the frequency increases. Moreover, at aparticular frequency, the output power P_(max) can depend on the totalmagnetic flux change in the solenoid, in one oscillation period, whichis directly related to the permeability μ of the magnetic cores.Therefore, multi-layer soft magnetic beams with a high permeabilityconstitute excellent candidates for the solenoid cores. In someembodiments, a multilayer structure of magnetic material generates amuch larger flux change than a single layer, as shown in FIG. 1 by theHigh-μ (1^(st) gen) device, which among other differences, uses a singlelayer core.

In some embodiments, the magnetic coupling between the fixed solenoids202 with multi-layer highly permeable cores, and the time varying biasmagnetic field generated by the vibrating magnetic core 208 results in alarge magnetic flux reversal and maximized flux change in the solenoids202, leading to a high maximum power of 610.62 mW, and a maximum powerdensity of 20.84 mW/cm³ at a frequency of 42 Hz.

FIG. 3A is a top-view image of an exemplary energy harvesting device300, and FIG. 3B is a side-view image of the exemplary energy harvestingdevice 300 of FIG. 3A. The device 300 includes solenoids 302A, 302B,each with a copper wire coil 304A, 304B formed around the core, andwrapping 306A, 306B made of a thin insulator (e.g., teflon, paper, etc.)to hold the respective copper wire coil 304A, 304B in place about thecore. In this example, each solenoid 302A, 302B core is a 28-layer highpermeability MuShield® material, with dimensions 2 cm×2 cm×0.002 inchfor each layer. In some embodiments, the copper wire coils 304A, 304Bare made of copper wire (e.g., with a diameter of 1 mm or 40 mils). Insome embodiments, the copper wires include 2-5 layers of copper coils,and each layer includes 20-50 turns around the core. The coil resistanceof each solenoid 302A, 302B is 1.3 Ohm. Each solenoid 302A, 302B is heldin place by a mount 308A, 308B made of a dielectric material (e.g.,acrylic, or other insulator material). In some embodiments, the copperwires are coated with a thin insulator.

The magnetic core 310 includes two SmCo hard magnets 312, 314 withdimensions 2.2 cm×1.3 cm×0.2 cm. The two magnets 312, 314 are joined bya non-magnetic spacer to produce a fringing field that is coupled to thesolenoids on the two ends of the hard magnets. The magnetic core 310 ismounted on spring 320, which has a circular cross-section. The magneticcore 310 can vibrate within the area formed by the mount 308A, 308B andsupports 316, 318. In this example, the device 300 is powered by avibrating stage that is driven by an audio power amplifier, and itsmechanical movement is monitored by an accelerometer. The voltage outputof the harvester 300 in the time domain is monitored by a digitaloscilloscope. Total volume of the energy harvester is 6.44 cm×3.25cm×1.4 cm=29.3 cm³, which includes the solenoids 302A, 302B, themagnetic core 310 and the gap between the solenoids 302A, 302B and themagnetic core 310.

FIG. 4 is a graph 400 of measured open circuit voltage (V) of the energyharvesting device 300 of FIGS. 3A-3B over time (s) using three differentsprings in accordance with certain embodiments. Each spring has adifferent resonance frequency: spring #1 has a resonance frequency of 27Hz, spring #2 has a resonance frequency of 33 Hz, and spring #3 has aresonance frequency of 42 Hz. For the first spring #1, the peak voltageis 1.18 V for an acceleration of 2 g (where g=9.8 m/s²), and the maximumoutput power on a 2.6 Ohm load is 133.88 mW. For the second spring #2,the peak voltage is 1.64 V for acceleration of 3 g, resulting in amaximum output power of 258.62 mW on a 2.6 Ohm load. For the thirdspring #3, the maximum induced voltage is 2.52 V for an acceleration of5 g, with the corresponding power 610.62 mW on a 2.6 Ohm load.Increasing acceleration values were applied to maintain the same sourcevibration amplitude. Considering that the total practical volume of thedevice is 29.3 cm³, this device demonstrated excellent performance withthe maximum power density of 20.84 mW/cm³ at 42 Hz. Graph 400demonstrates that a higher resonance frequency leads to a larger outputpower.

The Q factor of the harvester at 42 Hz was 16, which was obtained fromthe decay curve of output voltage when turning off the source. Almostthe entire device damping is generated from the mechanical collisionbetween the spring supported magnetic core and the solenoid supports.Therefore, other crafting techniques that reduce this mechanicalcollision could achieve a much higher Q factor while using a much lowerinput force or acceleration (e.g., by designing the magnetic core suchthat it floats along a rail, to include bearings to reduce the frictionagainst the surrounding supports, to include a material that reduces thefriction between the magnetic core and the surrounding supports, etc.).A simple relation between frequency and power can be derived fromEquation (3), as shown below in Equation (4), if all other parameterskept constant:

P _(max)˜(ΔM/ΔT)² ˜f ²   (4)

where:ΔM is the flux change per period;ΔT the period; andf is the frequency.

Measured test results confirm the parabolic curve fitting, as shown inFIG. 5, which is a graph 500 of the output power (mW) of the energyharvesting device achieved for the different frequencies (Hz) of thethree springs graphed in FIG. 4. In some embodiments, the vibrationenergy harvester design can accommodate different vibrating frequenciesof the environment by changing the spring that is connected to themagnetic core. For example, a larger vibration frequency of theenvironment (for a particular application) can induce a higher outputpower if matched with a spring with an appropriate resonance frequency.In some examples, if the vibration amplitude of the testing stage iskept the same, the output power and power density are proportional tothe second power of the vibration frequency. If P_(max)˜f² can beextrapolated to higher frequencies, a higher output power density can beachieved while maintaining a constant amplitude.

FIG. 6 is a graph 600 of the power density (mW/cm³) of the energyharvesting device based on the frequency (Hz). Graph 600 shows that theoutput power demonstrates a sagging rise before 42 Hz, which achieves amaximum output of 610.62 mW, and then rapidly declines afterwards. Theasymmetrical curve can be caused by the nonlinear oscillation, which canincrease the mechanical damping as the frequency ascends. The half-powerbandwidth of the device with spring #3 was measured to be 6 Hz, or ˜15%of the central frequency, which is much higher than the typical 2-5%bandwidth of typical piezoelectric cantilever-based energy harvesters.

Upon review of the description and embodiments of the present invention,those skilled in the art will understand that modifications andequivalent substitutions may be performed in carrying out the inventionwithout departing from the essence of the invention. Thus, the inventionis not meant to be limiting by the embodiments described explicitlyabove, and is limited only by the claims which follow.

What is claimed is:
 1. An energy harvesting device, comprising: a firstand second solenoid, each solenoid comprising (a) a wire coil wrappedaround (b) a high permeability core with two or more layers, and thefirst and second solenoid being disposed along a first path; and amagnetic core: disposed between the first and second solenoid such thatthe first solenoid is mounted on a first side of the magnetic core, andthe second solenoid is mounted on a second side of the magnetic core;and mounted on a support such that the magnetic core can vibrate along asecond path that intersects the first path, vibration of the magneticcore inducing a flux change in the first and second solenoids.
 2. Theenergy harvesting device of claim 1, wherein the magnetic core comprisesa first magnet.
 3. The energy harvesting device of claim 2, wherein themagnetic core comprises a second magnet disposed above the first magnetsuch that the first magnet and second magnet have anti-parallel moments.4. The energy harvesting device of claim 1, wherein the supportcomprises a spring.
 5. The energy harvesting device of claim 4, whereinthe spring comprises a circular cross-section.
 6. The energy harvestingdevice of claim 4, wherein the spring has a resonance frequency of 42Hz.
 7. The energy harvesting device of claim 6, wherein vibration of themagnetic core achieves a power output density of 20.84 mW/cm³.
 8. Theenergy harvesting device of claim 1, wherein each high permeability coreis a 28-layer core, each layer comprising dimensions 2 cm×2 cm×0.002inch.
 9. The energy harvesting device of claim 8, wherein the magneticcore comprises a second magnet, and the first and second magnets areSmCo magnets with dimensions 2.2 cm×1.3 cm×0.2 cm.
 10. The energyharvesting device of claim 9, wherein a total volume of the energyharvesting device is 6.44 cm×3.25 cm x1.4 cm =29.3 cm³.
 11. The energyharvesting device of claim 1, wherein the first solenoid, the secondsolenoid, and the support are mounted to a base such that the first pathis substantially parallel to the base, and the second path issubstantially perpendicular to the base.
 12. The energy harvestingdevice of claim 1, wherein the first and second solenoids comprise asame size.
 13. The energy harvesting device of claim 12, wherein thefirst and second solenoids comprise a same shape.
 14. The energyharvesting device of claim 12, further comprising joining the first andsecond solenoids in series to double a voltage of the energy harvestingdevice.
 15. In an energy harvesting device, comprising (1) a first andsecond solenoid, each solenoid comprising (a) a wire coil wrapped around(b) a high permeability core with two or more layers, and the first andsecond solenoid being disposed along a first path, and (2) a magneticcore disposed between the first and second solenoid such that the firstsolenoid is mounted on a first side of the first magnet, and the secondsolenoid is mounted on a second side of the first magnet, the magneticcore being mounted on a support such that the magnetic core can vibratealong a second path that is orthogonal to the first path, a methodcomprising: vibrating the magnetic core along the second path to inducea flux change in the first and second solenoids.
 16. The method of claim15, further comprising: vibrating the magnetic core at 42 Hz; andgenerating an output power of 610.62 mW.